Fig. REF (b) further shows the
mean central temperature \(\theta _c\)  as function of \(\theta _m\) , for both the 2D and the 3D cases.
We note that the collapse of the 3D data with the 2D data confirms
the similarity between 2D and 3D RBC for large \(Pr\)  [1]}.
One can observe two different regimes: in regime I, for low density inversion parameter \(0\le \theta _m \ll 1\) ,
the central temperature \(\theta _c\)  monotonically increases with increasing \(\theta _m\) , and all the data
collapse onto a single curve, independently of \(Ra\) . However, in regime II, for \(\theta _m\)  close to 1, with increasing \(\theta _m\) 
the central temperature \(\theta _c\)  extremely sharply drops to the value 1/2.
We denote the value of \(\theta _m\) , at which \(\theta _c\)  reaches 1/2
in regime II, as \(\theta _{m,c}\) ,
i.e., \(\theta _c(\theta =\theta _{m,c})=1/2\) .
It is clear that \(\theta _{m,c}\)  increases with increasing \(Ra\)  and approaches 1 for \(Ra\rightarrow \infty \) , implying that for strong enough thermal
driving the whole cell is filled with penetrative turbulence, even for large density inversion parameter close to 1.
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